What is a hypothesis

A falsifiable statement about what we believe will happen based on the theory we are trying to test.

Falsifiability

• We start from the assumption that our theory is wrong

Falsifiable

• We start from the assumption that our theory is wrong
• We assume there is no relationship

Falsifiable

• We start from the assumption that our theory is wrong
• We assume there is no relationship
• Our hypothesis is called the

alternative hypothesis or H1

Falsifiable

• We start from the assumption that our theory is wrong
• Our hypothesis is called the

alternative hypothesis or H1

• because it is the alternative to our assumption of no relationship

Falsifiable

• We start from the assumption that our theory is wrong
• Our hypothesis is called the:

alternative hypothesis or H1

• because it is the alternative to our assumption of no relationship. This is the:

null hypothesis or H0

Testing the null hypothesis

• Statistical tests show the degree of certainty that we can reject the null hypothesis

Testing the null hypothesis

• Statistical tests show the degree of certainty that we can reject the null hypothesis
• They show the likelihood that the alternative hypothesis is due to random chance

Testing the null hypothesis

• Statistical tests show the degree of certainty that we can reject the null hypothesis
• They show the probability that the alternative hypothesis is due to random chance
• When the probability, p, is below our pre-determined threshold, we reject the null hypothesis

Testing the null hypothesis

• Statistical tests show the degree of certainty that we can reject the null hypothesis
• They show the probability that the alternative hypothesis is due to random chance
• When the probability, p, is below our pre-determined threshold, we reject the null hypothesis
• If we reject the null hypothesis, the alternative hypothesis is true, right?

Testing the null hypothesis

• Statistical tests show the degree of certainty that we can reject the null hypothesis
• If we reject the null hypothesis, the alternative hypothesis is true, right?

NO!!!!

Rejecting the null hypothesis

If we reject the null we infer that the alternative hypothesis is approximately true within the probability we have chosen.

How do we get there?

How do we get from a sample with a correlation to talking about testing a hypothesis for a population?

How do we get there?

How do we get from a sample with a correlation to talking about testing a hypothesis for a population?

• Tying sample statistics to population parameters by Law of Large Numbers

Law of Large Numbers

Given a sample of independent and identically distributed values, the sample mean converges to the true mean.

Law of Large Numbers

• With a large enough sample size
• the sample mean will be close to the true mean for the population

How do we get there?

How do we get from a sample with a correlation to talking about testing a hypothesis for a population?

• Tying sample statistics to population parameters by Law of Large Numbers
• Larger sample size also reduces the standard error which is a special case of the standard deviation

Standard error

• The standard error is the standard deviation of the sampling distribution of a statistic
• Usually the standard error is the standard deviation of the sample mean
• Measures how accurately the sample measures the population
• Is also an element in the formula for the confidence interval and the z-score in hypothesis testing

How do we get there?

How do we get from a sample with a correlation to talking about testing a hypothesis for a population?

• Tying sample statistics to population parameters by Law of Large Numbers
• Larger sample size also reduces the standard error which is a special case of the standard deviation
• Tying our data to the probability distributions

Probability distributions

68-95-99.7 Rule

Probability distributions

68-95-99.7 Rule

            - Allows us to estimate probability based on distance from the mean

Probability distributions

68-95-99.7 Rule

            - Allows us to estimate probability based on distance from the mean
            - Applies to normal distribution
            

Probability distributions

The 68-95-99.7 Rule

            - Allows us to estimate probability based on distance from the mean
            - Applies to normal distribution
            - Basis for the actual decision rules using the *standard error* and the *z-score*
            

The 68-95-99.7 Rule

68-95-99.7 rule

Authorship, License, Credits

• Author: Tom Hanna

• Website: tomhanna.me

• License: This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.</>